What is the derivative of (3x+1((x^2+4))/((6x-5))) ?

The derivative of (3x+1((x^2+4))/((6x-5))) is (36x^3-39x^2-10x-84)/((6x-5)^2)

What is the first derivative of (3x+1((x^2+4))/((6x-5))) ?

The first derivative of (3x+1((x^2+4))/((6x-5))) is (36x^3-39x^2-10x-84)/((6x-5)^2)

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\frac{d}{d x} ((3 x + 1) \frac{( x ^{2} + 4 )}{( 6 x - 5 )})

\frac{36 x ^{3} - 39 x ^{2} - 10 x - 84}{( 6 x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} ((3 x + 1) \frac{( x ^{2} + 4 )}{( 6 x - 5 )})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x + 1, g = \frac{x ^{2} + 4}{6 x - 5}

= \frac{d}{d x} (3 x + 1) \frac{x ^{2} + 4}{6 x - 5} + \frac{d}{d x} (\frac{x ^{2} + 4}{6 x - 5}) (3 x + 1)

\frac{d}{d x} (3 x + 1) = 3

\frac{d}{d x} (\frac{x ^{2} + 4}{6 x - 5}) = \frac{6 x ^{2} - 10 x - 24}{( 6 x - 5 ) ^{2}}

= 3 \cdot \frac{x ^{2} + 4}{6 x - 5} + \frac{6 x ^{2} - 10 x - 24}{( 6 x - 5 ) ^{2}} (3 x + 1)

Simplify

3 \cdot \frac{x ^{2} + 4}{6 x - 5} + \frac{6 x ^{2} - 10 x - 24}{( 6 x - 5 ) ^{2}} (3 x + 1) : \frac{36 x ^{3} - 39 x ^{2} - 10 x - 84}{( 6 x - 5 ) ^{2}}

= \frac{36 x ^{3} - 39 x ^{2} - 10 x - 84}{( 6 x - 5 ) ^{2}}

What is the derivative of (3x+1((x^2+4))/((6x-5))) ?
The derivative of (3x+1((x^2+4))/((6x-5))) is (36x^3-39x^2-10x-84)/((6x-5)^2)
What is the first derivative of (3x+1((x^2+4))/((6x-5))) ?
The first derivative of (3x+1((x^2+4))/((6x-5))) is (36x^3-39x^2-10x-84)/((6x-5)^2)